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Unformatted text preview: IE 495 Lecture 24 November 28, 2000 Reading for This Lecture Primary Bazaraa, Sherali, and Sheti, Chapter 2. Chvatal, Chapters 6 and 7. Linear Programming Introduction Consider again the system Ax = b, A R m n , b R m . In this problem, there are either no solutions one solution infinitely many solutions (if n &gt; m) The problem of linear programming is min c T x s.t. Ax = b x 0 Applications of Linear Programming Linear programming is central to much of operations research. Many resource allocation problems can be described as linear programs. Example: The Diet Problem We have a set of nutrients with RDAs. We have a set of available foods. We have preference constraints which limit the intake of particular foods. We want to minimize our cost. Convex Sets A set S is convex x 1 , x 2 S, [0,1] x 1 + ( 1- 29 x 2 S If x = i x i , where i and i = 1 , then x is a convex combination of the x i 's . If the positivity restriction on is removed, then y is an affine combination of the x i 's ....
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